The invention relates generally to the field of plasma physics, and, in particular, to methods and apparati for confining plasma. Plasma confinement is particularly of interest for the purpose of enabling a nuclear fusion reaction.
Fusion is the process by which two light nuclei combine to form a heavier one. The fusion process releases a tremendous amount of energy in the form of fast moving particles. Because atomic nuclei are positively chargedxe2x80x94due to the protons contained thereinxe2x80x94there is a repulsive electrostatic, or Coulomb, force between them. For two nuclei to fuse, this repulsive barrier must be overcome, which occurs when two nuclei are brought close enough together where the short-range nuclear forces become strong enough to overcome the Coulomb force and fuse the nuclei. The energy necessary for the nuclei to overcome the Coulomb barrier is provided by their thermal energies, which must be very high. For example, the fusion rate can be appreciable if the temperature is at least of the order of 104 eVxe2x80x94corresponding roughly to 100 million degrees Kelvin. The rate of a fusion reaction is a function of the temperature, and it is characterized by a quantity called reactivity. The reactivity of a D-T reaction, for example, has a broad peak between 30 keV and 100 keV.
Typical fusion reactions include:
D+Dxe2x86x92He3(0.8 MeV)+n(2.5 MeV), 
D+Txe2x86x92xcex1(3.6 MeV)+n(14.1 MeV), 
D+He3xe2x86x92xcex1(3.7 MeV)+p(14.7 MeV), and 
p+B11xe2x86x923xcex1(8.7 MeV), 
where D indicates deuterium, T indicates tritium, xcex1indicates a helium nucleus, n indicates a neutron, p indicates a proton, He indicates helium, and B11 indicates Boron-11. The numbers in parentheses in each equation indicate the kinetic energy of the fusion products.
The first two reactions listed abovexe2x80x94the D-D and D-T reactionsxe2x80x94are neutronic, which means that most of the energy of their fusion products is carried by fast neutrons. The disadvantages of neutronic reactions are that (1) the flux of fast neutrons creates many problems, including structural damage of the reactor walls and high levels of radioactivity for most construction materials; and (2) the energy of fast neutrons is collected by converting their thermal energy to electric energy, which is very inefficient (less than 30%). The advantages of neutronic reactions are that (1) their reactivity peaks at a relatively low temperature; and (2) their losses due to radiation are relatively low because the atomic numbers of deuterium and tritium are 1.
The reactants in the other two equationsxe2x80x94D-He3 and p-B11xe2x80x94are called advanced fuels. Instead of producing fast neutrons, as in the neutronic reactions, their fusion products are charged particles. One advantage of the advanced fuels is that they create much fewer neutrons and therefore suffer less from the disadvantages associated with them. In the case of D-He3, some fast neutrons are produced by secondary reactions, but these neutrons account for only about 10 per cent of the energy of the fusion products. The p-B11 reaction is free of fast neutrons, although it does produce some slow neutrons that result from secondary reactions but create much fewer problems. Another advantage of the advanced fuels is that the energy of their fusion products can be collected with a high efficiency, up to 90 per cent. In a direct energy conversion process, their charged fusion products can be slowed down and their kinetic energy converted directly to electricity.
The advanced fuels have disadvantages, too. For example, the atomic numbers of the advanced fuels are higher (2 for He3 and 5 for B11). Therefore, their radiation losses are greater than in the neutronic reactions. Also, it is much more difficult to cause the advanced fuels to fuse. Their peak reactivities occur at much higher temperatures and do not reach as high as the reactivity for D-T. Causing a fusion reaction with the advanced fuels thus requires that they be brought to a higher energy state where their reactivity is significant. Accordingly, the advanced fuels must be contained for a longer time period wherein they can be brought to appropriate fusion conditions.
The containment time for a plasma is xcex94t=r2/D, where r is a minimum plasma dimension and D is a diffusion coefficient. The classical value of the diffusion coefficient is Dc=ai2/xcfx84ie, where ai is the ion gyroradius and xcfx84ie is the ion-electron collision time. Diffusion according to the classical diffusion coefficient is called classical transport. The Bohm diffusion coefficient, attributed to short-wavelength instabilities, is DB=(1/16)ai2 xcexa9i, where xcexa9i is the ion gyrofrequency. Diffusion according to this relationship is called anomalous transport. For fusion conditions, DB/Dc=(1/16)xcexa9ixcfx84ie≈108, anomalous transport results in a much shorter containment time than does classical transport. This relation determines how large a plasma must be in a fusion reactor, by the requirement that the containment time for a given amount of plasma must be longer than the time for the plasma to have a nuclear fusion reaction. Therefore, classical transport condition is more desirable in a fusion reactor, allowing for smaller initial plasmas.
In early experiments with toroidal confinement of plasma, a containment time of xcex94t≈r2/DB was observed. Progress in the last 40 years has increased the containment time to xcex94t≈1000r2/DB. One existing fusion reactor concept is the Tokamak. The magnetic field of a Tokamak 68 and a typical particle orbit 66 are illustrated in FIG. 5. For the past 30 years, fusion efforts have been focussed on the Tokamak reactor using a D-T fuel. These efforts have culminated in the International Thermonuclear Experimental Reactor (ITER), illustrated in FIG. 7. Recent experiments with Tokamaks suggest that classical transport, xcex94t≈r2/Dc, is possible, in which case the minimum plasma dimension can be reduced from meters to centimeters. These experiments involved the injection of energetic beams (50 to 100 keV), to heat the plasma to temperatures of 10 to 30 keV. See W. Heidbrink and G. J. Sadler, 34 Nuclear Fusion 535 (1994). The energetic beam ions in these experiments were observed to slow down and diffuse classically while the thermal plasma continued to diffuse anomalously fast. The reason for this is that the energetic beam ions have a large gyroradius and, as such, are insensitive to fluctuations with wavelengths shorter than the ion gyroradius (xcex less than ai). The short-wavelength fluctuations tend to average over a cycle and thus cancel. Electrons, however, have a much smaller gyroradius, so they respond to the fluctuations and transport anomalously.
Because of anomalous transport, the minimum dimension of the plasma must be at least 2.8 meters. Due to this dimension, the ITER was created 30 meters high and 30 meters in diameter. This is the smallest D-T Tokamak-type reactor that is feasible. For advanced fuels, such as D-He3 and p-B11, the Tokamak-type reactor would have to be much larger because the time for a fuel ion to have a nuclear reaction is much longer. A Tokamak reactor using D-T fuel has the additional problem that-most of the energy of the fusion products energy is carried by 14 MeV neutrons, which cause radiation damage and induce reactivity in almost all construction materials due to the neutron flux. In addition, the conversion of their energy into electricity must be by a thermal process, which is not more than 30% efficient.
Another proposed reactor configuration is a colliding beam reactor. In a colliding beam reactor, a background plasma is bombarded by beams of ions. The beams comprise ions with an energy that is much larger than the thermal plasma. Producing useful fusion reactions in this type of reactor has been infeasible because the background plasma slows down the ion beams. Various proposals have been made to reduce this problem and maximize the number of nuclear reactions.
For example, U.S. Pat. No. 4,065,351 to Jassby et al. discloses a method of producing counterstreaming colliding beams of deuterons and tritons in a toroidal confinement system. In U.S. Pat. No. 4,057,462 to Jassby et al., electromagnetic energy is injected to counteract the effects of bulk equilibrium plasma drag on one of the ion species. The toroidal confinement system is identified as a Tokamak. In U.S. Pat. No. 4,894,199 to Rostoker, beams of deuterium and tritium are injected and trapped with the same average velocity in a Tokamak, mirror, or field reversed configuration. There is a low density cool background plasma for the sole purpose of trapping the beams. The beams react because they have a high temperature, and slowing down is mainly caused by electrons that accompany the injected ions. The electrons are heated by the ions in which case the slowing down is minimal.
In none of these devices, however, does an equilibrium electric field play any part. Further, there is no attempt to reduce, or even consider, anomalous transport.
Other patents consider electrostatic confinement of ions and, in some cases, magnetic confinement of electrons. These include U.S. Pat. No. 3,258,402 to Farnsworth and U.S. Pat. No. 3,386,883 to Farnsworth, which disclose electrostatic confinement of ions and inertial confinement of electrons; U.S. Pat. No. 3,530,036 to Hirsch et al. and U.S. Pat. No. 3,530,497 to Hirsch et al. are similar to Farnsworth; U.S. Pat. No. 4,233,537 to Limpaecher, which discloses electrostatic confinement of ions and magnetic confinement of electrons with multipole cusp reflecting walls; and U.S. Pat. No. 4,826,646 to Bussard, which is similar to Limpaecher and involves point cusps. None of these patents consider electrostatic confinement of electrons and magnetic confinement of ions. Although there have been many research projects on electrostatic confinement of ions, none of them have succeeded in establishing the required electrostatic fields when the ions have the required density for a fusion reactor. Lastly, none of the patents cited above discuss a field reversed configuration magnetic topology.
The field reversed configuration (FRC) was discovered accidentally around 1960 at the Naval Research Laboratory during theta pinch experiments. A typical FRC topology, wherein the internal magnetic field reverses direction, is illustrated in FIG. 8 and FIG. 10, and particle orbits in a FRC are shown in FIG. 11 and FIG. 14. Regarding the FRC, many research programs have been supported in the United States and Japan. There is a comprehensive review paper on the theory and experiments of FRC research from 1960-1988. See M. Tuszewski, 28 Nuclear Fusion 2033, (1988). A white paper on FRC development describes the research in 1996 and recommendations for future research. See L. C. Steinhauer et al., 30 Fusion Technology 116 (1996). To this date, in FRC experiments the FRC has been formed with the theta pinch method. A consequence of this formation method is that the ions and electrons each carry half the current, which results in a negligible electrostatic field in the plasma and no electrostatic confinement. The ions and electrons in these FRCs were contained magnetically. In almost all FRC experiments, anomalous transport has been assumed. See, e.g., Tuszewski, beginning of section 1.5.2, at page 2072.
To address the problems faced by previous plasma containment systems, a system and apparatus for containing plasma are herein described in which plasma ions are contained magnetically in stable, large orbits and electrons are contained electrostatically in an energy well. A major innovation of the present invention over all previous work with FRCs is the simultaneous electrostatic confinement of electrons and magnetic confinement of ions, which tends to avoid anomalous transport and facilitate classical containment of both electrons and ions. In this configuration, ions may have adequate density and temperature so that upon collisions they are fused together by the nuclear force, thus releasing fusion energy.
In a preferred embodiment, a plasma confinement system comprises a chamber, a magnetic field generator for applying a magnetic field in a direction substantially along a principle axis, and an annular plasma layer that comprises a circulating beam of ions. Ions of the annular plasma beam layer are substantially contained within the chamber magnetically in orbits and the electrons are substantially contained in an electrostatic energy well. In one aspect of one preferred embodiment a magnetic field generator comprises a current coil. Preferably, the system further comprises mirror coils near the ends of the chamber that increase the magnitude of the applied magnetic field at the ends of the chamber. The system may also comprise a beam injector for injecting a neutralized ion beam into the applied magnetic field, wherein the beam enters an orbit due to the force caused by the applied magnetic field. In another aspect of the preferred embodiments, the system forms a magnetic field having a topology of a field reversed configuration.
Also disclosed is a method of confining plasma comprising the steps of magnetically confining the ions in orbits within a magnetic field and electrostatically confining the electrons in an energy well. An applied magnetic field may be tuned to produce and control the electrostatic field. In one aspect of the method the field is tuned so that the average electron velocity is approximately zero. In another aspect, the field is tuned so that the average electron velocity is in the same direction as the average ion velocity. In another aspect of the method, the method forms a field reversed configuration magnetic field, in which the plasma is confined.
In another aspect of the preferred embodiments, an annular plasma layer is contained within a field reversed configuration magnetic field. The plasma layer comprises positively charged ions, wherein substantially all of the ions are non-adiabatic, and electrons contained within an electrostatic energy well. The plasma layer is caused to rotate and form a magnetic self-field of sufficient magnitude to cause field reversal.
In other aspects of the preferred embodiments, the plasma may comprise at least two different ion species, one or both of which may comprise advanced fuels.
Having a non-adiabatic plasma of energetic, large-orbit ions tends to prevent the anomalous transport of ions. This can be done in a FRC, because the magnetic field vanishes (i.e., is zero) over a surface within the plasma. Ions having a large orbit tend to be insensitive to short-wavelength fluctuations that cause anomalous transport.
Magnetic confinement is ineffective for electrons because they have a small gyroradiusxe2x80x94due to their small massxe2x80x94and are therefore sensitive to short-wavelength fluctuations that cause anomalous transport. Therefore, the electrons are effectively confined in a deep potential well by an electrostatic field, which tends to prevent the anomalous transport of energy by electrons. The electrons that escape confinement must travel from the high density region near the null surface to the surface of the plasma. In so doing, most of their energy is spent in ascending the energy well. When electrons reach the plasma surface and leave with fusion product ions, they have little energy left to transport. The strong electrostatic field also tends to make all the ion drift orbits rotate in the diamagnetic direction, so that they are contained. The electrostatic field further provides a cooling mechanism for electrons, which reduces their radiation losses.
The increased containment ability allows for the use of advanced fuels such as D-He3 and p-B11, as well as neutronic reactants such as D-D and D-T. In the D-He3 reaction, fast neutrons are produced by secondary reactions, but are an improvement over the D-T reaction. The p-B11 reaction, and the like, is preferable because it avoids the problems of fast neutrons completely.
Another advantage of the advanced fuels is the direct energy conversion of energy from the fusion reaction because the fusion products are moving charged particles, which create an electrical current. This is a significant improvement over Tokamaks, for example, where a thermal conversion process is used to convert the kinetic energy of fast neutrons into electricity. The efficiency of a thermal conversion process is lower than 30%, whereas the efficiency of direct energy conversion can be as high as 90%.
Other aspects and features of the present invention will become apparent from consideration of the following description taken in conjunction with the accompanying drawings.